code: def add_implicit_on_curves(p):
      q = list(p)
      count = 0
      num_offcurves = len(p) - 2
      for i in range(1, num_offcurves):
          off1 = p[i]
          off2 = p[i + 1]
          on = off1 + (off2 - off1) * 0.5
          q.insert(i + 1 + count, on)
          count += 1
      return q
  
file_path: catboost/contrib/python/fonttools/fontTools/qu2cu/qu2cu.py
imports: from fontTools.misc.bezierTools import splitCubicAtTC
  from collections import namedtuple
  import math
  from typing import List, Tuple, Union
label_desc: Use image node_id 4 for calling a global function with example usage: add_implicit_on_curves(p) and returns: q